Bayesian ranking and selection methods using hierarchical mixture models in microarray studies.

The main purpose of microarray studies is screening to identify differentially expressed genes as candidates for further investigation. Because of limited resources in this stage, prioritizing or ranking genes is a relevant statistical task in microarray studies. In this article, we develop 3 empirical Bayes methods for gene ranking on the basis of differential expression, using hierarchical mixture models. These methods are based on (i) minimizing mean squared errors of estimation for parameters, (ii) minimizing mean squared errors of estimation for ranks of parameters, and (iii) maximizing sensitivity in selecting prespecified numbers of differential genes, with the largest effect. Our methods incorporate the mixture structures of differential and nondifferential components in empirical Bayes models to allow information borrowing across differential genes, with separation from nuisance, nondifferential genes. The accuracy of our ranking methods is compared with that of conventional methods through simulation studies. An application to a clinical study for breast cancer is provided